Band-gap voltage references are used as voltage references in electronic systems. The energy band-gap of Silicon is on the order of 1.2 V, and is independent from temperature and power-supply variations. Bipolar transistors have a negative temperature drift with respect to their base-emitter voltage (Vbe) such that their Vbe decreases as the operating temperature increases on the order of −2 mV/deg C. However, the thermal voltage (Vt) of a bipolar transistor has a positive temperature drift (Vt=kT/q) such that Vt increases as temperature increases. The positive temperature drift in the thermal voltage (Vt) may be arranged to compensate the negative temperature drift in the bipolar transistor's base-emitter voltage (Vbe). Band-gap reference circuits use the inherent characteristics of bipolar transistors to compensate for temperature effects and provide a stable operating voltage over various power-supply and temperature ranges.
An example of a modern band-gap reference circuit is illustrated as circuit 500 in FIG. 5. As shown in the figure, two bipolar transistors (Q1, Q2) are arranged with a common base that is connected to VDD. Two resistors (R1, R2) are series connected between the emitter of the first bipolar transistor (Q1) and the reference output (VREF). Another resistor (R3) is connected between the emitter of the second bipolar transistor (Q2) and the reference output (VREF). An error amplifier (EAMP) is used to adjust the voltage of the reference output (VREF) through feedback. At steady-state, the voltage at the common point of resistors R1 and R2 is the same as the voltage at the emitter of the second bipolar transistor (Q2). The two bipolar transistors (Q1, Q2) are arranged to provide a ten-to-one (10:1) current density difference with respect to one another (Q2 to Q1). The ten-to-one current density results in a 60 mV difference between the base-emitter voltages of two bipolar transistors (ΔVbe=Vt*ln(A1/A2)=26 mV*ln(10)=60 mV, at room temperature. A1 and A2 are the respective emitter areas of bipolar transistors Q1 and Q2. Current I1 is set to equal current I2 by means of resistors R2, R3, and feedback operation of error amplifier EAMP. The 60 mV difference appears across the first resistor (R1). The voltage between VDD and the output of the error amplifier corresponds to a reference voltage (VREF) that is given as VREF=Vbe+X*Vt, where X is a constant that is used to scale the temperature correction factor. The temperature correction factor (X) is adjusted by the ratio of the resistors ((R2/R1)*ln(A1/A2)). Typical temperature corrected reference voltages of 1.25 V are achieved by his configuration.